systems of equations with different slopes and different y-intercepts have more than one solution

Always
sometimes
Never

I believe it is Never or sometimes
I am leaning towards Never

If you have different slopes, then you will have one solution of intersection. So you would be correct.

ANONYMOUS

If you have two lines with different slopes and different y-intercepts, they MUST intersect and you will ALWAYS have a solution

You are correct, the correct answer is "Never." Systems of equations with different slopes and different y-intercepts never have more than one solution.

You are correct, the answer is sometimes.

When two systems of equations have different slopes and different y-intercepts, they represent two lines on a graph that are not parallel. In some cases, these lines may intersect at a single point, which means they have one solution. However, there are cases where the lines are coincident, meaning they have the same equation and infinitely many solutions.

So, while it is never true that systems of equations with different slopes and different y-intercepts have exactly one solution, it is sometimes true that they have more than one solution.